Computing generators of the ideal of a smooth affine algebraic variety

• Autores: Blanco, C.; Jeronimo, G.; Solernó, P.
• Año de publicación: 2004
• Idioma: inglés
• Tipo de recurso: artículo
• Fuente: J. Symb. Comput. 2004;38(1):843-872
• Materia: Computation of the radical of a regular ideal; Efficient generation of polynomial ideals; Number and degree of generators of polynomial ideals; Regular signs; Straight-line programs
• Institución: Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales

Let K be an algebraically closed field, V ⊂ Kn be a smooth equidimensional algebraic variety and I (V) ⊂ K[x1,...,xn] be the ideal of all polynomials vanishing on V. We show that there exists a system of generators f1,...,fm of I (V) such that m ≤ (n - dim V) (1 + dim V) and deg(fi) ≤ deg V for i = 1,...,m. If char(K) = 0 we present a probabilistic algorithm which computes the generators f1,..., fm from a set-theoretical description of V. If V is given as the common zero locus of s polynomials of degrees bounded by d encoded by straight-line programs of length L, the algorithm obtains the generators of I (V) with error probability bounded by E within complexity s(ndn)O(1)log2 (⌈1/E⌉)L. © 2004 Elsevier Ltd. All rights reserved.
Fil:Blanco, C. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.
Fil:Jeronimo, G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.
Fil:Solernó, P. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.